Question 1205635
mike will catch up to aaron when they have both traveled the same distance.
mike will have been on the road 1 hour less than aaron because he started an hour later.


rate * time  distance is the basic formula used.


for aaron, you get r * t = d
r is the rate
t is the time in hours
d is the distance in miles.


for mike, you get r * (t-1) = d
r is the rqte
t-1 is the time in hours.
d is the distance in miles.


these these two equations need to be solved simultaneously.


for aaron, the equation becomes 55 * t = d
for mike, the equation becomes 70 * (t-1) = d


since they are both equal to d, you can set 55 * t equal to 70 * (t-1)
simplify to get 55 * t = 70 * t - 70
subtract 55 * t from both sides of the equation and add 70 to both sides of the equation to get 70 = 15 * t
solve for t to get t = 4.66666666.....


aaron's equation becomes 55 * 4.6666666.... = d
mike's equation becomes 70 * 3.6666666.... = d


solve for d to get d = 256.666666.... in both equations.


your solution is that mike will overtake aaron in 3 and 2/3 hours.